Rigid Body Dynamics
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A Uniform Rod 2 ft Long, Weighting 5 lbs, Is Revolving 60 Times A Minute About One End. Calculate Its Moment Of Inertia And Kinetic Energy.
Ans. Here the mass of the uniform rod M=5 lbs,length of the rod is l=2 ft.The rod is rotating about one end with frequency =1 rev./sec.The angular velocity is We…
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Two Particles Of Masses ‘m’ And ‘M’ Are At A Distance ‘d’ Apart. Calculate The Moment Of Inertia Of The System About An Axis Passing Through The Centre Of Mass And Perpendicular To The Line Joining The Two Masses. If ‘ν’ Be The Frequency Of Revolution, Then Also Calculate The Rotational Kinetic Energy Of The System.
Ans. Here the two masses ‘m‘ and ‘M‘ are at a distance d apart. Let us consider, O be the centre of mass of the system of these two masses,…
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Two Parallel Circular Wheels, Each Of Mass ‘M’ And Radius ‘R’ And Filled With Weightless Spokes Are Rigidly Joined Together By A Weightless Rod Of Length 2R Passing Through The Centre Of The Wheels Perpendicular To Their Planes. Calculate The Moment Of Inertia Of The Wheels About An Axis Passing Perpendicular Through The Centre Of The Rod.
Ans. Here, two wheels each of mass M and radius R are rigidly connected by a weightless rod of length 2R. The moment of inertia of each wheel about their…
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A Circular Disc Of Mass ‘M’ And Radius ‘r’ Is Set Rolling On A Table. If ‘ω’ Be The Angular Velocity, Calculate Its Total Energy ‘E’.
Ans. When a circular disc of mass M and radius r rolls on a table, then its total kinetic energy E will be, = (Energy due to linear motion) +…
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A Solid Spherical Ball Rolls On A Table, Find The Ratio Of Its Translational And Rotational Kinetic Energies And The Total Energy Of The Spherical Ball. What Fraction Of The Total Energy Is Rotational?
Ans. Let us consider a spherical ball of radius r and mass M. If v be the linear velocity of the ball then the translational kinetic energy of the ball…
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A Cylinder Has A Mass ‘M’, Length ‘l’ And Radius ‘a’. Find The Ratio Of ‘l’ To ‘a’ If The Moment Of Inertia About An Axis Through The Centre And Perpendicular To The Length Is Minimum
Ans. Here, the mass of the cylinder is M, radius is a and length is l. If be the density of material of the cylinder, then the mass of the…
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Centres Of Four Solid Spheres Of Diameter ‘2a’ And Mass ‘m’ Make Square Of Side ‘b’. Calculate The Moment Of Inertia Of The System About One Side Of The Square.
Ans. Four spheres, each of mass m and radius a, are placed at the corners of the square of side b, as shown in Fig.1. We know that the moment…
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A System Consists Of Three Identical Spheres Of Radius ‘r’ And Mass ‘m’ Placed With Their Centres Forming The Vertices Of An Equilateral Triangle Of Side ‘a’. Calculate The Moment Of Inertia Of The About An Axis Passing Through The Centre Of Gravity Of The System And Perpendicular To The Place Of The Centres.
Ans. Three spheres of radius ‘r‘ and mass ‘m‘ placed with their centres at the vertices of an equilateral triangle ABC. Here G is the centre of gravity. From Fig.…